In U.S. Pat. No. 3,517,678 granted to Gilsdorf June 30, 1970, there is shown a handgrip for a crutch adapted to be mounted between spaced, parallel, generally vertical anterior and posterior supports of a crutch and provided with a hand-supporting surface contoured to accommodate substantially the entire planar surface of the hand. The handgrip therein illustrated is structured at its posterior side to provide a recess of rectangular cross section for non-rotatably receiving one of the crutch supports, has a transverse planar surface contoured to accommodate substantially the entire planar surface of the hand and is of solid block-like construction. The contoured hand-supporting surface shown therein is entirely satisfactory from the standpoint of providing a supporting surface for the hand; however, the structure as configured can only be used with a crutch wherein the supports are of rectangular cross section. The patented structure has the disadvantage that it is solid and, therefore, does not provide for gripping, is wasteful of material, and, finally, is not so structured as to enable disposing it in a nested position between the supports when the crutch is not in use. It is the purpose of this invention to overcome these disadvantages by so structuring the grip that it can be used with crutches having supports of rectangular or circular cross section, to reduce the cost by recessing its underside so as to economize in the amount of material used in its manufacture, to provide for better grasping of the structure, and to so mount the structure as to enable fixing it in a horizontal position for use and rotating it to a vertical nested position for non-use.